You can do both the confed and rebel alien mission strings.
Early in the game, you must accept the Confed Transfer Documents, but not complete it. Look around for the Rebel Transfer Documents mission, accept it, then complete both missions. This will set the bits marking you as both a rebel and a confed.
As cable_guy noted, keeping up your standing with both governments will be difficult. You will need to be upstanding citizen everywhere, so you must avoid the assassination, destroy convoy, destroy escort carrier, and defend planet from rebel/confed attack missions. You must also avoid engaging rebel/confed warships unless a mission specifically requires it.
I cannot keep up the legal status beyond the confed particle beam mission. After that, I drift into working exclusively for the rebels. The only time (months ago) I maintained the required standing long enough to reach the alien missions for both governments, EV crashed when I attempted accept the destroy alien mission the second time around.
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